246 Prof. Barnard on a modification of the Ericsson Engine. 
Put 7'= temperature of air in working cylinder. 
6 = temperature of the weather. 
= temperature of air after compression by the condens- 
ing cylinder.* 
©= number of degrees of heat required to double vol. of 
air, at original temperature of 32° F. 
g= density of the atmospheric air at the time, which. 
may always be assumed =1. 
o’= density of air in reservoir, which (9 being 1) we have 
mn 
already seen must be equal to _~ 
‘ nue 
Hence, (II), #=(040)(<) —6=(6+0)( 
It is evident that, 
ae 
a): —9. 
l 
TO ; 
n—1= O16 (940 )n—O=T, 
r Jy-1 
And gS es 
0+ (0+46)mrinr! 
(T+ 0)b-? _/T+0\2/1\% 
Oe ae ad wn (PENH 
Hence, putting 7 and m, each =3, as before, assuming 0=28° 
(weather temp. =60° F. ), and 7'=450° (being =482° F’.—as high 
a heat as is probably safe), we shall have n=1-55 very nearly. 
Returning to equation (IL) with this value of the co-efficient of 
expansion, we have &=116°-5, or 148°-5 above the zero of Fah- 
renheit. 
Equation (I) furnishes also the tension due to this value of 7, 
which is 27-2 lbs. to the square inch. 
The formula heretofore given to express the mean pressure 
will now no longer be applicable; since, in the construction of 
that formula, density was assumed as a just measure of tension. 
t 
That is to say, 7 Was put equal to . of Poisson’s formula; where- 
e gf \? 
meh oh (®) - ‘Moreover the area of the logarithmic curve will no 
longer truly express the elastic force exerted by the air during 
expansion or compression. Instead of this we must substitute 
that of a different curve, whose absciss, 2, is the altitude of the 
column of air undergoing change of density, and whose ordinate 
is ¢’’, the tension corresponding to that altitude. Fr the positive 
term of variable pressure, we have the maximum tension =4, 
I 
and by (1), 
rd 2)’. 
ma 
* These temperatures are to be estimated from 32° ahrenheit, and not from the 
miu of tak ccc. : 
